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Abstract Root Subgroups and Simple Groups of Lie-Type: 95 (Monographs in Mathematics, 95) - Tapa dura
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Sinopsis
This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.
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"The book is well written: the style is concise but not hard and most of the book is not too difficult to read for a graduate student. Some parts of it are certainly suited for a class."
--Mathematical Reviews
Reseña del editor
This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.
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Abstract Root Subgroups and Simple Groups of Lie-Type (Monographs in Mathematics, Band 95).
Librería: ANTIQUARIAT Franke BRUDDENBOOKS, Lübeck, Alemania
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Gebundene Ausgabe, Gr.-8°. Condición: Sehr gut. 2001. 402 S. Das Buch ist in sehr gutem, sauberen Zustand. Gebundenes Buch mit Original-Schutzumschlag. Dieser mit minimalen. Randläsuren. -----Inhalt:. It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson. I Rank One Groups.- 1 Definition, examples, basic properties.- 2 On the structure of rank one groups.- 3 Quadratic modules.- 4 Rank one groups and buildings.- 5 Structure and embeddings of special rank one groups.- II Abstract Root Subgroups.- 1 Definitions and examples.- 2 Basic properties of groups generated by abstract root subgroups.- 3 Triangle groups.- 4 The radical R(G).- 5 Abstract root subgroups and Lie type groups.- III Classification Theory.- 1 Abstract transvection groups.- 2 The action of G on ?.- 3 The linear groups and EK6.- 4 Moufang hexagons.- 5 The orthogonal groups.- 6 D4(k).- 7 Metasymplectic spaces.- 8 E6(k),E7(k) and E8(k).- 9 The classification theorems.- IV Root involutions.- 1 General properties of groups generated by root involutions.- 2 Root subgroups.- 3 The Root Structure Theorem.- 4 The Rank Two Case.- V Applications.- 1 Quadratic pairs.- 2 Subgroups generated by root elements.- 3 Local BN-pairs.- References.- Symbol Index. ISBN: 9783764365325 Due to new EU packaging regulations, we are currently unable to ship to many EU countries. Shipping to Germany, the Netherlands, Ireland, Finland, and the Baltic states is possible. Deliveries to border-based parcel lockers or cross-border parcel forwarding services remain possible. Shipping to all countries outside the EU also remains possible. Sprache: Englisch Gewicht in Gramm: 1043. Nº de ref. del artículo: 669031
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Abstract Root Subgroups & Simple Groups Of Lie-type (monographs In Mathematics)
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Abstract Root Subgroups & Simple Groups Of Lie-type (monographs In Mathematics)
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Abstract Root Subgroups and Simple Groups of Lie-Type (Monographs in Mathematics, 95)
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Abstract Root Subgroups and Simple Groups of Lie Type
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Springer, Basel, Birkhäuser Basel, Birkhäuser Aug 2001, 2001
ISBN 10: 3764365323
ISBN 13: 9783764365325
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite 'nearly' simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called 'internal geometric analysis' by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson. 389 pp. Englisch. Nº de ref. del artículo: 9783764365325
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Abstract Root Subgroups and Simple Groups of Lie-Type
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Nº de ref. del artículo: 5279435
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Abstract Root Subgroups and Simple Groups of Lie-Type
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Condición: New. Systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M Aschbacher, B Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. Series: Monographs in Mathematics. Num Pages: 389 pages, biography. BIC Classification: PBG. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 23. Weight in Grams: 747. . 2001. Hardback. . . . . Nº de ref. del artículo: V9783764365325
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